# Infinite quotient rule?

Calculus Level 3

$F(x) = \cfrac{x}{x + \cfrac{x}{x + \cfrac{x}{x + \cfrac{x }{._{._.}}} } }$

If the value of first derivative of $$F(x)$$ at $$x = 1$$ can be expressed as $$\dfrac{a\sqrt b - b}{c}$$ for integers $$a,b$$ and $$c$$, find the value of $$a+b+c$$.

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